Cell decomposition for P‐minimal fields

In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for p‐adically closed fields. We work here with the notion of P‐minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a P‐minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8] (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental Investigations on Polymeric Foams

The knowledge of the material behaviour of polymeric foams and their experimental investigation is the starting point for the structure of the chosen constitutive equations and for the following identification of the material constants therein. Especially for the parameter identification, it is necessary to make an adequate set of experimental data available. In this regard, it is important that the experiments make the different kinds of material behaviour visible like elastic, plastic or viscous material properties. For this reason, the foam is observed under uniaxial tension and compression and under simple shear tests combined with different deformation states in axial direction. Unfortunately, due to different reasons, e.g., the foam must be sticked on the fastener to realize the tests mentioned above, it is very difficult to initialize a homogenous deformation state in the specimen. Therefore, the experiments are recorded with a standard digital camcorder to get local information of the deformation state by tracking single points with algorithms of the digital image processing. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Permeability of Clustered Fiber Networks: Modeling of the Unit Cell

The paper is focused on estimating the permeability of a clustered fiber network by variational methods. First, a laminar flow in ducts is considered by using polynomial trial functions. Then, a longitudinal flow through a square array is described by expanding the flow-rate field in trigonometric and Laurent series. Finally, a formal scheme for estimating the longitudinal permeability in a cluster with an irregular distribution of fibers is given. The irregular distribution is modeled by setting an individual effective radius for each fiber and then letting this fiber reach its minimum gravitational energy. The results obtained here form a basis for future predictions of the permeability of fibrous reinforcements.     

Transport of Mass,Momentum and Energy through Periodic Open Cell Metal Foams Applied in Catalysis

An ODE model to predict the temperature field of periodic open cell metal foams applied in catalysis as carrier structures is presented. The catalytic and highly endothermic reaction takes place in a porous layer which surround the struts of the foam and releases gas from a fluid. The one-dimensional model includes dependencies of the foam structure (strut radius, shape of strut), process conditions (surrounding velocity, surrounding fluid: liquid and/or gas), chemical conditions (reaction enthalpy, activation energy) and material parameters (thermal conductivity, density, viscosity). This makes it possible to estimate optimal parameters, that are able to provide sufficient heat to the reaction. The advantage of this model is the substantial time saving in contrary to three dimensional finite volume simulations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cell decomposition and definable functions for weak p‐adic structures

We develop a notion of cell decomposition suitable for studying weak p‐adic structures (reducts of p‐adic fields where addition and multiplication are not (everywhere) definable). As an example, we consider a structure with restricted addition.     

A note on second‐order finite‐difference schemes on uniform meshes for advection‐‐diffusion equations

An artificial‐viscosity finite‐difference scheme is introduced for stabilizing the solutions of advection‐diffusion equations. Although only the linear one‐dimensional case is discussed, the method is easily susceptible to generalization. Some theory and comparisons with other well‐known schemes are carried out. The aim is, however, to explain the construction of the method, rather than considering sophisticated applications. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 581–588, 1999     

Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces on domains

The purpose of this paper is to develop a theory of the Besov‐Morrey spaces and the Triebel‐Lizorkin‐Morrey spaces on domains in R ⁿ. We consider the pointwise multiplier operator, the trace operator, the extension operator and the diffeomorphism operator. Not only to domains in R ⁿ we extend our definition of function spaces to compact oriented Riemannian manifolds. Among the properties above, the result for the trace operator is in particular interesting, which reflects the property of the parameters p, q in the Morrey space ??^p_q (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Regularity criterion on energy equality for compressible Cahn‐Hilliard‐Navier‐Stokes equations

This paper is concerned with the compressible Cahn‐Hilliard‐Navier‐Stokes system. We establish a sufficient regularity condition such that every weak solution conserves its energy equality for every t > 0. Our approach is based on the commutator and mollification approximation.     

Students' Concepts‐ and Theorems‐in‐Action on a Novel Task About Similarity

Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts‐in‐action and theorems‐in‐action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric and multiplicative reasoning at the same time in order to construct similar figures? We found that students used concepts of scaling and proportional reasoning, as well as the concept of circle and theorems about similar triangles, in their work on the problem. Students relied not only on visual perception, but also on numeric reasoning. Moreover, students' use of multiplicative and proportional concepts supported their geometric constructions. Knowledge of the concepts and ideas that students have available when working on a task about similarity can inform instruction by helping to ground formal introduction of new concepts in students' informal prior experiences and knowledge.     

Exponentially many 4‐list‐colorings of triangle‐free graphs on surfaces

Thomassen proved that every planar graph G on n vertices has at least distinct L‐colorings if L is a 5‐list‐assignment for G and at least distinct L‐colorings if L is a 3‐list‐assignment for G and G has girth at least five. Postle and Thomas proved that if G is a graph on n vertices embedded on a surface Σ of genus g, then there exist constants such that if G has an L‐coloring, then G has at least distinct L‐colorings if L is a 5‐list‐assignment for G or if L is a 3‐list‐assignment for G and G has girth at least five. More generally, they proved that there exist constants such that if G is a graph on n vertices embedded in a surface Σ of fixed genus g, H is a proper subgraph of G, and ϕ is an L‐coloring of H that extends to an L‐coloring of G, then ϕ extends to at least distinct L‐colorings of G if L is a 5‐list‐assignment or if L is a 3‐list‐assignment and G has girth at least five. We prove the same result if G is triangle‐free and L is a 4‐list‐assignment of G, where , and .     

Fixed‐point theorem for a generalized almost Hardy‐Rogers‐type F contraction on metric‐like spaces

In this paper, we introduce some fixed‐point theorems for a generalized almost Hardy‐Rogers‐type F contraction in a metric‐like space and give an example to illustrate these main results. Moreover, we show the applications of electric circuit equations, second‐order differential equations, and fractional differential equations. Our results improve, generalize, and extend the corresponding results in literature.     

Four‐terminal reducibility and projective‐planar wye‐delta‐wye‐reducible graphs

A graph is YΔY‐reducible if it can be reduced to a vertex by a sequence of series‐parallel reductions and YΔY‐transformations. Terminals are distinguished vertices, that cannot be deleted by reductions and transformations. In this article, we show that four‐terminal planar graphs are YΔY‐reducible when at least three of the vertices lie on the same face. Using this result, we characterize YΔY‐reducible projective‐planar graphs. We also consider terminals in projective‐planar graphs, and establish that graphs of crossing‐number one are YΔY‐reducible. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 83–93, 2000     

Sobolev‐Jawerth embedding of Triebel‐Lizorkin‐Morrey‐Lorentz spaces and fractional integral operator on Hardy type spaces

A Sobolev type embedding for Triebel‐Lizorkin‐Morrey‐Lorentz spaces is established in this paper. As an application of this result, the boundedness of the fractional integral operator on some generalizations of Hardy spaces such as Hardy‐Morrey spaces and Hardy‐Lorentz spaces are obtained.     

A note on triangle‐free quasi‐symmetric designs

Triangle‐free quasi‐symmetric 2‐ (v, k, λ) designs with intersection numbers x, y; 0<x<y<kand λ>1, are investigated. It is proved that λ?2y ? x ? 3. As a consequence it is seen that for fixed λ, there are finitely many triangle‐free quasi‐symmetric designs. It is also proved that: k?y(y ? x) + x. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 19:422‐426, 2011     

2‐connected 7‐coverings of 3‐connected graphs on surfaces

An m‐covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3‐connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2‐connected 7‐covering with at most 6k ? 12 vertices of degree 7. We also construct, for every surface F² with Euler genus k ≥ 2, a 3‐connected graph G on F² with arbitrarily large representativity each of whose 2‐connected 7‐coverings contains at least 6k ? 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003     

Two types of upper semi‐continuity of bi‐spatial attractors for non‐autonomous stochastic p‐Laplacian equations on

We consider the long time behavior of solutions for the non‐autonomous stochastic p‐Laplacian equation with additive noise on an unbounded domain. First, we show the existence of a unique ‐pullback attractor, where q is related to the order of the nonlinearity. The main difficulty existed here is to prove the asymptotic compactness of systems in both spaces, because the Laplacian operator is nonlinear and additive noise is considered. We overcome these obstacles by applying the compactness of solutions inside a ball, a truncation method and some new techniques of estimates involving the Laplacian operator. Next, we establish the upper semi‐continuity of attractors at any intensity of noise under the topology of . Finally, we prove this continuity of attractors from domains in the norm of , which improves an early result by Bates et al.(2001) who studied such continuity when the deterministic lattice equations were approached by finite‐dimensional systems, and also complements Li et al. (2015) who discussed this approximation when the nonlinearity f(·,0) had a compact support. Copyright © 2017 John Wiley & Sons, Ltd.     

High‐resolution monotone schemes based on quasi‐characteristics technique

In this article, we consider a new technique that allows us to overcome the well‐known restriction of Godunov's theorem. According to Godunov's theorem, a second‐order explicit monotone scheme does not exist. The techniques in the construction of high‐resolution schemes with monotone properties near the discontinuities of the solution lie in choosing of one of two high‐resolution numerical solutions computed on different stencils. The criterion for choosing the final solution is proposed. Results of numerical tests that compare with the exact solution and with the numerical solution obtained by the first‐order monotone scheme are presented. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 262–276, 2001     

Stability of multi‐group coupled systems on networks with multi‐diffusion based on the graph‐theoretic approach

In this paper, the issue of stability of multi‐group coupled systems on networks with multi‐diffusion (MCSNMs) is mainly analyzed. Utilizing graph theory, a novel and practical method of constructing a proper Lyapunov function for the MCSNMs is presented. Furthermore, based on the graph‐theoretic approach and the proposed Lyapunov function, sufficient criteria, in the term of Lyapunov function and coefficients of the system, respectively, are derived to ensure the stability of the MCSNMs. Apart from accessibility to checking, the proposed results can generalize the corresponding results published in a previous time. Finally, the effectiveness and feasibility of the obtained results are demonstrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.